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arXiv · 2306.06114

Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures

Anatolij Dvurečenskij·Omid Zahiri
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Abstract

In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, the main aim is to continue to study the structure of pseudo MV-algebras with square roots focusing on their new characterizations. The paper is divided into two parts. In the first part, we investigate the relationship between a pseudo MV-algebra with square root and its corresponding unital $\ell$-group in the scene of two-divisibility. In the present second part, we find some conditions under which a particular class of pseudo MV-algebras can be embedded into pseudo MV-algebras with square roots. We introduce and investigate the concepts of a strict square root of a pseudo MV-algebra and a square root closure, and we compare both notions. We show that each MV-algebra has a square root closure. Finally, using the square root of individual elements of a pseudo MV-algebra, we find the greatest subalgebra of a special pseudo MV-algebra with weak square root.

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Anatolij Dvurečenskij, Omid Zahiri. 2023-06-01. Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures. https://arxiv.org/abs/2306.06114

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